WORK . 16' Therefore the work done against the gravitational force ii taking a body from one position to another depends only upoi the vertical height through which the body is raised and no upon the path. 130. Dimensions and Units of Work. Work is a scala magnitude and has for its dimensions [ML2T~2]. The C.G.8 unit of work is the erg. It equals the work done by a fore of one dyne in displacing a particle through a distance o one centimeter, measured along its line of action. It i symbolized by -:~. The erg is a small unit, therefor sec.2 a larger unit called the joule is also used. 1 joule = 107 ergs. The British unit of work is the foot-pound (ft.4b.). It i the work done against the gravitational attraction of th earth in lifting one pound through a vertical distance o one foot. Since the work done in lifting bodies is mgh, w can express the foot-pound in terms of the fundamenta units, thus 1 ft. Ib. = 1 pd. X 32.2;^ X 1 ft. = 32.2 where pd. represents the pound-mass. 131. Work Done by Components of Force.The work don by a force F in giving a particle a displacement ds is F cos 6 <& where 0 is the angle between F and ds. Let X, Y, and Z b the rectangular components of F, then the direction of I X Y 7 is defined by its direction cosines -=,, and . Therefor b b F if Z, m, and n denote the direction cosines of ds, we get . -.X . Y . Z* cos0=Z- + m~ +n~ * See Appendix Aiv.